You are not limited to three components. The a,b part is to show that uses of the comma outside the argument of \vektor are allowed.

The fact that \left-\right make a group is fundamental, because this ensures that changes to the \mathcode of the comma are confined to that place. The special mathcode "8000 means that the comma behaves like an active character; the definition of the active comma is given in an indirect way, so as not to conflict with possible other meanings as an active character.